16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 2.1.4

Vector Spaces

Mathematics — Linear Algebra · vector-space-axioms-check

Problem

Let

V

be the set of all pairs

(x, y)

of real numbers, and let

F

be the field of real numbers. Define

(x, y) + (x_1, y_1) = (x + x_1, y + y_1)

c(x, y) = (cx, y).

V

, with these operations, a vector space over the field of real numbers?